Modeling with Linear Systems Answers

The Carson family paid $192 for two adult and three youth tickets to an amusement park. At the same park, the Davis family paid $148 for one adult and four youth tickets. Let x represent the cost of an adult ticket, and let y represent the cost of a youth ticket. Which system of equations can be used to find the cost of each ticket?

A school drama department sells 40 more student tickets than adult tickets. Charging $8 for adult tickets and $6 for student tickets, the drama department raises a total of $1,920 in ticket sales. Let x represent the number of adult tickets sold and y represent the number of student tickets sold. Which system of equations can be used to find how many of each ticket is sold?

Lisa leaves a gas station and drives at an average rate of 50 mi/hr. Keisha leaves the gas station one hour later and drives along the same route at an average rate of 60 mi/hr. Let d represent the distance driven in miles and t represent the time since Lisa left the gas station. Which system of equations can be used to find how long after Lisa left the gas stations that she is passed by Keisha?

Pam laid three times as many tiles on Saturday as she laid on Sunday. If Pam laid 80 tiles over the weekend altogether, how many tiles did she lay on Saturday?

Reese read twice as many pages Saturday than she read Sunday. If she read a total of 78 pages over the weekend, how many pages did Reese read Sunday?

A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width in inches of the picture frame, and let l represent the length in inches. Which system of equations can be used to find the dimensions of the picture frame?

The concession stand at the local high school sells pretzels and lemonade. The total cost of two pretzels and a lemonade is $5.75. The total cost of two lemonades is $0.25 more than the cost of a pretzel. What is the cost of a pretzel?

Miguel and Beth like to play video games together. Miguel has m video games, and Beth has b video games. Miguel has 4 more video games than Beth, and together they have a total of 24 video games. Which system of equations can be used to find how many video games belong to each friend?

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original number. What is the original number?

The given system of equations models the coins in a jar containing n nickels, d dimes, and q quarters. Which statement is modeled by one of the equations in the system?